Design for Fatigue Loading - Calculator for the Goodman Criterion |
This section carries out an assessment of a proposed design against the 'Goodman criterion'. This criterion is usually represented graphically by plotting the mean stress that the component is subjected to (Sigma_{m}) along the horizontal axis and the alternating stress amplitude, Sigma_{a}, along the vertical axis.
The UTS of the material (S_{u}) is marked on the horizontal axis and the fatigue endurance strength, S_{e}, is marked on the vertical axis and the Goodman line connects these two points.
It should be noted that in real components the fatigue endurance strength will be modified (reduced) below that achieved with polished test specimens (due to surface, size, load, temperature and miscellaneous effects) and the theoretical endurance strength must be multiplied by these fatigue strength reducing factors before being marked on the vertical axis as the one end of the Goodman line.
Components subjected to cyclic stress regimes which when plotted on this diagram are below and to the left of the Goodman line are safe designs whereas those subjected to stresses that when plotted are above / to the right of the Goodman line are unsafe designs.
If the stresses on a safe design are marked as a point, B, on the diagram and a line drawn through this point and parallel to the Goodman line, the distance this line is away from the Goodman line is a measure of the factor of safety, or the design factor, n, of this particular part.
The design factor in the calculation below assumes ratio of the stress amplitude/mean stress remains constant.
Notes about inputs required for this calculation:
The fatigue endurance strength for polished test specimens, S_{e}. In the In the absence of specific data, a value of 0.5 times the UTS can be used for steels with a UTS of 1400 MPa or less. For steels with a UTS of greater than 1400 MPa, then a value of 700 MPa should be used.
Where there is a stress concentration present, the inverse of this stress concentration factor can be used as the 'miscellaneous strength reducing factor', k_{e}, below.
Is this design factor adequate?
David J Grieve, updated: 13th July 2004, original: 20th September 1999.